13717
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 19
- Digital Root
- 1
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 4
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 15840
- Proper Divisor Sum (Aliquot Sum)
- 2123
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 11760
- Möbius Function
- -1
- Radical
- 13717
- Omega Function (Ω)
- 3
- Little Omega Function (ω)
- 3
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- no
- Perfect Cube
- no
- Pentagonal Number
- no
- Hexagonal Number
- no
- Lucas Number
- no
- Tetrahedral Number
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- yes
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 32
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Numbers k such that k^16 == 1 (mod 17^3).at n=41A056088
- Numbers k such that k^18 == 1 (mod 19^3).at n=35A056089
- a(1) = 1; a(n+1) = (product{k|n} a(k)) (sum{j|n} 1/a(j)), where both the product and sum are over the positive divisors of n.at n=10A068342
- Numbers k that divide 2^(k+3) - 1.at n=45A069927
- a(n) is the smallest number k such that GCD of n values of prime(j)-1 for successive j values starting with k is greater than 2.at n=9A080373
- Sum of the sizes of the Durfee squares of all partitions of n.at n=29A115995
- Sum of the squares of the quadratic nonresidues of prime(n).at n=13A125617
- 11 times pentagonal numbers: 11*n*(3n-1)/2.at n=29A153449
- a(n) = 361*n - 1.at n=37A158308
- a(n) = 38*n^2 - 1.at n=18A158596
- (A178476(n)-3)/9.at n=0A178486
- a(n) is the smallest k such that prime(k+i) = 1 (mod 6) for i = 0, 1,...,n-1.at n=8A247816
- a(n) is the smallest k such that prime(k+i) = 1 (mod 6) for i = 0, 1,...,n-1.at n=9A247816
- Index of the first prime which starts a run of n consecutive primes all congruent to each other mod 3 (or mod 6).at n=8A276414
- Index of the first prime which starts a run of n consecutive primes all congruent to each other mod 3 (or mod 6).at n=9A276414
- Number of vertices formed in a square by straight line segments when connecting the four corner vertices to the points dividing the sides into n equal parts.at n=29A355949
- Number of integer partitions of n of length > 2 whose second differences have median 0.at n=36A360682
- a(n) = Sum_{k=0..n} floor(sqrt(k))^4.at n=38A363498
- Dirichlet g.f.: zeta(s-3)^2 * (1 - 2^(4-s)) / zeta(s).at n=18A369101
- a(n) = Sum_{1 <= x_1, x_2, x_3 <= n} gcd(x_1, x_2, x_3, n)^3.at n=18A372928